UC Riverside

Ultra-cold fermionic atoms trapped in optical lattices may be a candidate for

the discovery of new novel phenomena in condensed matter systems.

Experiments afford the creation of virtually any lattice geometry, and physical

parameters of tight binding type lattice models can be acurately and easily

tuned. Although some theoretical work has been conducted, few have used the

power of the functional renormalization group method to unearth rigorous

methods for determining collective many-body phases in this regime. Motivated by

recent theoretical achievements, we investigate novel condensed matter systems

involving interacting fermions which are engineered to be confined in different

dimensions. In this sense, we seek low energy effective theories for

low-dimensional fermionic lattice systems embedded into higher dimensional

lattice systems, and show how tuning physical quantities, such as the filling

or density, can have dramatic effects on the behavior of the lower dimensional

system.